computational methods in molecular biophysics (examples of solving real biological problems) example...
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Computational methods in molecular biophysics (examples of solving real biological problems)
EXAMPLE I: THE PROTEIN FOLDING PROBLEM
Alexey Onufriev, Virginia Tech
www.cs.vt.edu/~onufriev
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OUTLINE:
• Folding proteins in ``virtual water”. Energy landscapes.
• Insights into the function of bacteriorhodopsin – the smallest solar panel.
• Understanding stability of proteins from bacteria living underextreme conditions (high salt).
Claims: 1. The use of detailed, atomic resolution models is often critical.
2. Simple physics works on very complex biological systems.
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Protein Structure in 3 steps.
Amino-acid #1 Amino-acid #2
Peptide bond
Step 1. Two amino-acids together (di-peptide)
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Step 2: Most flexible degrees of freedom:
Protein Structure in 3 steps.
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Protein Structure in 3 steps.
Sometimes, polypeptide chain forms helical structure:
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THEME I. Protein folding using the GB
MET—ALA—ALA—ASP—GLU—GLU--….
Experiment: amino acid sequence uniquely determines protein’s 3D shape (ground state).
Nature does it all the time. Can we?
Amino-acid sequence – translated genetic code.
How?
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The magnitude of the protein folding challenge:
Why bother: protein’s shape determines its biological function.
A small protein is a chain of ~ 50 mino acids (more for most ).
Assume that each amino acid has only 10 conformations (vast underestimation)
Total number of possible conformations: 1050
Say, you make one MC step per femtosecond.
Exhaustive search for the ground state will take 1027 years.
Enormous number of the possible conformations of the polypeptide chain
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Finding a global minimum in a multidimensional case is easy only when the landscape is smooth. No matter where you start (1, 2 or 3), you quickly end up at the bottom -- the Native (N), functional state of the protein.
Fre
e en
ergy
Folding coordinate
1
2
3
Adopted from Ken Dill’s web site at UCSF
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Adopted from Dobson, NATURE 426, 884 2003
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Realistic landscapesare much more complex, with multiple local minima –folding traps.
Adopted from Ken Dill’s web site at UCSF
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Adopted from Ken Dill’s web site at UCSF
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Each atom moves by Newton’s 2nd Law: F = ma
E =
+-
+ …
x
YPrinciples of Molecular Dynamics (MD):
F = dE/drSystem’s energy
Kr2
Bond stretching+ A/r12 – B/r6
VDW interaction
+ Q1Q2/r Electrostatic forces
Bondspring
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Computational advantages of representing
water implicitly, via a continuum solvent model
Explicit water
Large computational cost. Slow dynamics.
Implicit water as dielectric continuum
Low computational cost. Fast dynamics.
Other advantages: 1. Instant dielectric response => no water
equilibration necessary.2. No viscosity => faster conformational
transitions.3. Solvation in an infinite volume => no
boundary artifacts. 4. Solvent degrees of freedom taken into
account implicitly => easy to estimate total energy of solvated system.Electrostatic Interactions are key!
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Solvation energy of individual ion
+
+
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The generalized Born approximation (GB):
qi qj
rij
molecule
Vacuum part
Solvent polarization, W
Function to be determined.
Total electrostaticenergy
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The “magic” formula:
f = [ rij2 + RiRjexp(-rij
2/4RiRj) ]1/2 /Still et al. 1990 /
i j And when they fuse into one, and Born’s formula is recovered
i jInterpolates between the case when
atoms are far from each otherand Coulomb’s law is recovered
rij
0 f rij E ~ 1/r
0 1f (RiRj)1/2 E ~ 1/R
details: Onufriev et al. J. Phys. Chem. 104, 3712 (2000) Onufriev et al. J. Comp. Chem. 23, 1297 (2002) Onufriev et al. Proteins, 55, 383 (2004)
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Simulated Refolding pathway of the 46-residue protein. Molecular
dynamics based on AMBER-7
NB: due to the absence of viscosity, folding occurs on much shorter time-scale than in an experiment.
Movie available at: www.scripps.edu/~onufriev/RESEARCH/in_virtuo.html
1 3 5 0 1 2 3 4 5 6
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Folding a protein in virtuo using Molecular Dynamics based on the Generalized Born
(implicit solvation) model.
Simulation time: overnight on 16 processors.
Protocol details: AMBER-7 package, parm-94 force-field. New GB model.
Protein to fold: 46 -residue protein A (one of the guinea pigs in folding studies).
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Recent landmark attempt to fold a (36 residue) protein in virtuo using Molecular Dynamics:
Duan Y, Kollman, P Science, 282 740 (1998).
Simulation time: 3 months on 256 processors = 64 years on one processor.
Result: partially folded structure.
Problem: explicit water simulation are too expensive computationally – can’t wait long enough.
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4 5 6 7
The bottom of the folding funnel.